Other
Players

return to Variations on Go

We can form a
single united body,
while the enemy must split up into fractions.
Hence there will be a whole pitted against separate parts of a whole,
which means that we shall be many to the enemy's few.
[Sun Tzu, The Art of War - VI .14]

In
traditional GO, there are just two opponent players, each one must defeat the other in
order to win. Things may change completely if the number of players changes. I will
consider 3 to 8 different players. In the following images, the 3rd player is red, the 4th
is blue and the 5th is green.

After that, I'm going to approach
the multiplayer problem in two other different dimensions. The movement type and the
possibility of cooperation. Moves may be sequential (just like typical Go) or parallel,
and players may cooperate in taking other prisoners (a kind of a local alliance to destroy
some mutual enemies). The super KO rule should be enforced on every variant (no
board repetition is allowed).

Non
cooperative and Sequential Multiplayer Go

A 3 player Go should have the weaker
players move first. If the players have the same strength, one way to compensate is to
oblige the first player to pass in the 3rd turn.

A 4 player Go should also have the weaker
players move first. If the players have the same strength, one way to compensate is to
oblige the first and second player to pass in the 3rd turn.

The rule for 5 to 8 player Go, should give the
5th to 8th player a double move in the first turn, in order to compensate the lack of
corners for those players. A typical opening for 5 player Go should be something like
this:

The 5th player chooses to create an influence
between the positional strongest pair (the 1st and 3rd players). Then, the game proceeds
at one stone per player per turn.

The game should be very chaotic for more than 8
players. Probably, more than 4 players is already too much for a 19x19 board. Of course,
larger boards may be used for larger set of players.

Multiplayer (Non Coop) Go

All Go rules apply, except:

The first turn movements are defined above.

If a piece has no liberty due to two or more different
stones, it is removed and eliminated (no one gets that prisoner).

Cooperative
and Sequential Multiplayer Go

In Go, each player is fighting all others in the
sense that only one is going to win. In this variants, players may cooperate with each
other. First we must define what cooperation means:

a) Tactical Cooperation, means that two or more
players may encircle and capture stones from other players. If N players capture M stones,
each player gets the larger integer smaller than M/N stones, and the rest goes to the one
who dropped the last stone that did the capture. At the end of game, the shared territory
values the larger integer smaller than M/N to each player and the rest does not go to
anyone. The proportion of stones used in the capture of each player is irrelevant. The
captured pieces are chosen first by the last turn player (e.g., if the 1st and 3rd player
do a capture, the 3rd player chooses first what prisoners colors he wants).

Another way to deal with prisoners is presented
by Allan Crossman (which adds
a new tension to define what player will waste a move to capture stones): It
doesn't matter who gets the prisoners. At the end of the game, the prisoners
are simply put back in the territory of their own color, just like in two
player go with territory counting. Only in this way is it possible for
multiplayer go to have the same result whether territory or area scoring is
used. I think this is a very desirable feature.

b) Strategic Cooperation, means that at the
end of game, two or more players may unite their territories and prisoners (discounting
each other prisoners) in order to get more than 5/12 of the game total points. 5/12 is the
middle value between 1/3 (too easy) and 1/2 (too hard). If a solo victory means 1 point, a
shared N player victory means 1/N points for each one (it does not matter which one of the
allies has more, all players get the same points). Of course, if two alliances get more
than 5/12 of the total points, wins the one with more points.

Tactical Cooperation

There are 4 players (black, white, red and blue). If Red
or Blue play at [1], they will capture the white stone and black will get nothing.

If Blue plays at [2], the 2 white stones are
captured (Red receives one stone and Blue receives another). If Red plays at [2], he and
Black will capture the 3 stones (2 for red and one for black) and Black is the last to
choose.

If Black or Blue plays at [3], each one receives
one white stone. If Red plays at [3] he will gain 2 white stones.

If no alliances occur, Red will win (13+4=17 points).
However, if an alliance can get 74*(5/12) = 30.8 points, they will win. If Black allies
White then they would add 10 neutral territories and subtract the 5 white prisoners of
black, so 8 points for black, 15 for white plus 10 new territories, i.e., 33 points. They
can achieve a 2 way victory, so each one gets 1/2 point. They have a sure win, since a Red
+ Blue alliance would get only a total of 28 points.

Multiplayer (Coop) Go

All Go rules apply, except:

Tactical and strategic cooperation between players is
allowed.

Non
cooperative and Parallel Multiplayer Go

In Go, the moves are sequential. Each player
waits for his turn. If we define parallel moves, a player only knows the opponents actual
moves at the same time he makes his own move.

There is just a problem when two or more stones
tries to occupy the same cell. If that happens, all those moves are not made (i.e., those
players pass). This adds to Go a new kind of risk: if a drop is expected at cell C, will a
player take the chance of loose one move?

The set of rules are stated below:

Multiplayer (Parallel & Non
Coop) Go

All Go rules apply, except:

All moves on the same turn are simultaneous.

Stone drops to the same cell are not made.

All pieces with no liberties are removed.

Parallel Go Examples

If White plays at [1] and Black at [2], then one white
and one black stone are captured (top right position). If also Red plays at [3], then
there are an extra white stone captured (bottom right position).

Cooperative
and Parallel Multiplayer Go

This one inherits the rules from Parallel Go and
Cooperative Go. The only difference is that when capturing, the rest of the M/N division
goes to the players that dropped the last stones, if this division (rest/N) is greater
than one. The rest of the rest is eliminated.

Parallel Cooperative Go
Examples

If Black plays at [1] and White
at [2], they will capture 5 stones (3 blues and 2 reds). Since they are just 2, each one
receives 2 stones (5/2). Since the rest is 1 stone,
that divided by 2 is less than one, then one captured stone will be eliminated. White
chooses first what stones he wants, then Black. The remaining stone is then eliminated.

If Red plays at [3] and White plays at [4], the black
stone is eliminated. If also Blue plays at [3], then the red and blue moves are not made,
and the black stone are in Atari (with 3 white stones around it).